# A method for picking park rates

Concerning time binning of park rates, I will use integer n to represent a bin of length t days at rate R and C for total cost to the Nu network:

• n-1 is of length 0.5*t
• If you vote for R at n, there is no reason not to vote for R/2 at n+1 because C=Rt = (R/2)(2t)
• The inverse (2R at n-1) cannot be extrapolated because we don’t know the rate at t/2
• This means there is no reason not to vote for a very small park rate at 64 years if you vote for any park rate at all.
• R’.n can represent R for bin n after time t.n.

Without knowing something about what’s going on with Nu and the open market, it’s difficult to go further. So let me restrict my discussion to the case of increasing park rates.

• assume: R’.n > R.n and R.(n+1) = (R.n)/2
• C.(n+1) = R.(n+1)*(2t.n)
• C.n+C’.n = (R.n+R’.n)*t.n
• C.n + C’.n > C.(n+1)

This situation is bad for Nu, it means that it was more profitable to park for shorter periods than to keep the bits parked. If R.(n+1) = (R.n+R’.n)/2, the pathways would be the same.

I think the way to interpret this is that you should choose the shortest period you are willing to provide parking for. For the next highest bin, guess what the minimum rate will do between now and that next bin and take the average. For the next next highest, do the same thing but use the next highest bin instead.

Example:
I am willing to speculate that I would pay someone 12.5% to hold NBT for 11.4 days.
In 11.4 days, I think we will need to be near 17.5%, so I will vote for 15% for 22.8 days.
In 22.8 days, the fork auction might hurt, we should be near 20%, I vote 17.5% 1.5 month.
In 1.5 months, B&C will still be getting set up, lets vote 20% for 3 months.
In 3 months, things should be settling down, I think 15%, let’s vote 17.5% on 6 months.
In 6 months, we’ll be getting back down there near 7.5%, I vote 12.5% for the year.
In 1 year, we’ll be around 0%, let’s vote 6.25% on 2 years for an even number.
In 2 years, still 0%, vote 3.125% on 4 years.

This example assumes I’m updating continuously. The rate of the lowest bin is the most important factor here.

In your example above, wouldn’t it be rational to stop providing park rates at durations longer than 6 months? That is the period that would provide the maximum expected payout. If we pretend a user is willing to park 5.00 NBT, he would not park for a longer duration (1 year vs. 6 months) for a shorter expected payout (0.15 NBT vs. 0.31 NBT, very roughly).

Any rates offered beyond six months should result in the same expected payout, if the network is willing to provide a maximum of 0.31 NBT paid for 5.00 NBT parked. So, if 12.5% is set for 6 months, 6.25% would be set for 1 year, and 3.125% set for 2 years. A more simple way to look at it is that no rates should be offered past 6 months as a rational user would simply select 6 months due to the absence of negative utility accrued from not having access to the funds at longer durations.

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Oh, shoot, my math is wrong, let me fix that.
By the way, in my example 12.5% is set for the year while 17.5% is set for 6 months.

There is still the consideration of choosing 6 months for a lower interest rate than 3 months when you anticipate that there might be no interest rates at all in less than 3 months time.

I choose 3 months at 20% and 6 months at 17.5%. This is because I think that if someone parks for 3 months, they’ll find the park rates lower and will only be able to park for say 15%. In that case, the person who parks 3 months at 20% and another 3 months at 15% gets the same reward as the person who parks for 6 months at 17.5%.

When choosing the rate for a time bin, it should be the average of the shorter bin and where you think the shorter bin will be after the shorter time. So to get the 1 year rate, you take the 6 month rate and average it with where you think the 6 month rate will be in 6 months.

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